CBSE · Class 6-12

Class 12 · Mathematics (041)

Unit 10 · Class 12Mathematics (041)

Vectors and Three-Dimensional Geometry

Vectors

Vector algebra: addition, scalar and cross products, projections.

Lessons

4 concepts

1
Vector Basics
Magnitude $|\vec a|$ , unit vector $\hat a = \vec a / |\vec a|$ .
2
Dot Product
$\vec a \cdot \vec b = |\vec a||\vec b|\cos\theta$ ; used to find angle and projection.
3
Cross Product
$|\vec a \times \vec b| = |\vec a||\vec b|\sin\theta$ ; direction given by right-hand rule.
4
Applications
Area of parallelogram $= |\vec a \times \vec b|$ ; area of triangle $= \tfrac{1}{2}|\vec a \times \vec b|$ .

Skills to practise

Skill · medium

Vectors — Practice (coming soon)

Practice bank for this unit is in progress. You can still read the lessons above.